Name: capacitors in series and parallel
Uploaded: 2024-04-11T12:48:39.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.6

IPC.6.A

Equivalent Capacitance

Consider a complex capacitor network with three groups of capacitors connected in parallel, and these groups are then connected in series with each other. Determine the equivalent capacitance between the terminals of this intricate circuit.
To solve this, the group at the bottom of the circuit, consisting of four capacitors connected in parallel, is analyzed first. The sum of their capacitance gives an equivalent capacitance, represented by a single capacitor C3.
Next, the middle group, having three capacitors in parallel, is considered. Again, adding up their capacitances gives the equivalent capacitance C2.
Finally, consider the top group, which has two capacitors in parallel. The equivalent capacitance is calculated and represented with one capacitor, C1.
Now, the complex circuit has been simplified into three capacitors connected in series.
To determine the equivalent capacitance for this series combination, the sum of the reciprocals of each capacitance is taken, resulting in the inverse of the equivalent capacitance.
Upon rearranging the terms, the equivalent capacitance of the entire circuit between the terminals is obtained.

equivalent capacitance

From the study of resistive circuits, it is understood that employing a series-parallel combination serves as an effective strategy for simplifying circuits. Capacitors can be arranged within a circuit in one of two ways: a series configuration or a parallel configuration. The way these capacitors are connected to a battery will influence both the potential drop across each individual capacitor and the size of the charge that each capacitor can store. This is determined by the specific type of connection in place. To simplify this scenario, the combination of capacitors can be substituted with a single equivalent capacitor. This equivalent capacitor is able to store an identical amount of charge as the original combination when subjected to the same potential difference.
When there is a parallel connection of N capacitors, they all share the same voltage across them. The equivalent capacitance for such a configuration is given by
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It is crucial to note that the equivalent capacitance of N capacitors connected in parallel equals the total of their individual capacitances.
Transitioning now to the scenario where N capacitors are interconnected in a series, it is observed that the same current i, and consequently the same charge, flows through all the capacitors. The equivalent capacitance of this setup is represented as
<img alt="Parallel capacitance equation; &#931;(1/C) for capacitors in series; formula for total capacitance." src="/files/ftp_upload/15087/15087_PT_Equation_2.svg" style="text-align: center; height: 32px;" data-altupdatedat="1761848533000" data-alt="Equation2" />
In contrast to the parallel configuration, the equivalent capacitance of capacitors connected in series is calculated as the reciprocal of the sum of the reciprocals of each capacitor's individual capacitance.

Consider a complex capacitor network with three groups of capacitors connected in parallel, and these groups are then connected in series with each other. ...

Education

JoVE Core

Electrical Engineering

Unit 1

Energy Storage Elements

KEY TERMS AND CONCEPTS

capacitors in series and parallel

Capacitors in series and parallel can be simplified by replacing the group with one equivalent capacitor. This equivalent capacitor stores the same charge as the original network when the same potential difference is applied. The idea helps make complex capacitor circuits easier to analyze.

In a parallel connection, capacitors share the same voltage across each branch. The equivalent capacitance of N capacitors in parallel is the sum of their individual capacitances. This type of connection increases the total ability of the circuit to store charge.

In a series connection, the same current flows through each capacitor, and the same charge passes through them. The equivalent capacitance for N capacitors in series is found from the reciprocal of the sum of the reciprocals of each capacitance. This result is different from the parallel case and gives a smaller effective capacitance.

Capacitors in Series and Parallel

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Capacitors in series and parallel can be simplified by replacing the group with one equivalent capacitor. This equivalent capacitor stores the same charge as the original network when the same potential difference is applied. The idea helps make complex capacitor circuits easier to analyze. In a parallel connection, capacitors share the same voltage across each branch. The equivalent capacitance of N capacitors in parallel is the sum of their individual capacitances. This type of connection...

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key terms and concepts

Learn how capacitors behave in series and parallel, and how to find equivalent capacitance by adding capacitances in parallel or using reciprocals in series.

Capacitors in Series and Parallel | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

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Capacitors in Series and Parallel

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